Question

Integrate the following

Answer 1

\[\int\limits_{}^{} \frac{ 4}{ \sqrt{3-4x^{2}} } dx\]

Answer 2

\[\int\frac{4}{\sqrt{3-4x^2}}dx\\
4\int\frac{1}{\sqrt{3-4x^2}}dx\]
Make the following substitution:
\[x=\frac{\sqrt{3}}{2}\sin t\\
dx=\frac{\sqrt{3}}{2}\cos t\;dt\]
The integral then becomes
\[4\int\limits\frac{1}{\sqrt{3-4\left(\frac{\sqrt{3}}{2}\sin t\right)^2}}\left(\frac{\sqrt{3}}{2}\cos t\;dt\right)\]

Answer 3

Oh actually I figured it out after, what i was expected to do was to use arcsinx to solve. Thanks though!

Answer 4

Using this substitution will give you an answer in terms of arcsinx (after a few steps of simplification, of course), but I think there is some method of substitution directly involving arcsine. I'm just more familiar with this method.

You're welcome.